Evaluate
\frac{75000}{2131}\approx 35.194744252
Factor
\frac{2 ^ {3} \cdot 3 \cdot 5 ^ {5}}{2131} = 35\frac{415}{2131} = 35.19474425152511
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\begin{array}{l}\phantom{4262)}\phantom{1}\\4262\overline{)150000}\\\end{array}
Use the 1^{st} digit 1 from dividend 150000
\begin{array}{l}\phantom{4262)}0\phantom{2}\\4262\overline{)150000}\\\end{array}
Since 1 is less than 4262, use the next digit 5 from dividend 150000 and add 0 to the quotient
\begin{array}{l}\phantom{4262)}0\phantom{3}\\4262\overline{)150000}\\\end{array}
Use the 2^{nd} digit 5 from dividend 150000
\begin{array}{l}\phantom{4262)}00\phantom{4}\\4262\overline{)150000}\\\end{array}
Since 15 is less than 4262, use the next digit 0 from dividend 150000 and add 0 to the quotient
\begin{array}{l}\phantom{4262)}00\phantom{5}\\4262\overline{)150000}\\\end{array}
Use the 3^{rd} digit 0 from dividend 150000
\begin{array}{l}\phantom{4262)}000\phantom{6}\\4262\overline{)150000}\\\end{array}
Since 150 is less than 4262, use the next digit 0 from dividend 150000 and add 0 to the quotient
\begin{array}{l}\phantom{4262)}000\phantom{7}\\4262\overline{)150000}\\\end{array}
Use the 4^{th} digit 0 from dividend 150000
\begin{array}{l}\phantom{4262)}0000\phantom{8}\\4262\overline{)150000}\\\end{array}
Since 1500 is less than 4262, use the next digit 0 from dividend 150000 and add 0 to the quotient
\begin{array}{l}\phantom{4262)}0000\phantom{9}\\4262\overline{)150000}\\\end{array}
Use the 5^{th} digit 0 from dividend 150000
\begin{array}{l}\phantom{4262)}00003\phantom{10}\\4262\overline{)150000}\\\phantom{4262)}\underline{\phantom{}12786\phantom{9}}\\\phantom{4262)9}2214\\\end{array}
Find closest multiple of 4262 to 15000. We see that 3 \times 4262 = 12786 is the nearest. Now subtract 12786 from 15000 to get reminder 2214. Add 3 to quotient.
\begin{array}{l}\phantom{4262)}00003\phantom{11}\\4262\overline{)150000}\\\phantom{4262)}\underline{\phantom{}12786\phantom{9}}\\\phantom{4262)9}22140\\\end{array}
Use the 6^{th} digit 0 from dividend 150000
\begin{array}{l}\phantom{4262)}000035\phantom{12}\\4262\overline{)150000}\\\phantom{4262)}\underline{\phantom{}12786\phantom{9}}\\\phantom{4262)9}22140\\\phantom{4262)}\underline{\phantom{9}21310\phantom{}}\\\phantom{4262)999}830\\\end{array}
Find closest multiple of 4262 to 22140. We see that 5 \times 4262 = 21310 is the nearest. Now subtract 21310 from 22140 to get reminder 830. Add 5 to quotient.
\text{Quotient: }35 \text{Reminder: }830
Since 830 is less than 4262, stop the division. The reminder is 830. The topmost line 000035 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 35.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}